TSTP Solution File: SET902+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET902+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:45:25 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 20 unt; 0 def)
% Number of atoms : 109 ( 91 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 117 ( 52 ~; 37 |; 27 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 5 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
file('/tmp/tmpdblVMp/sel_SET902+1.p_1',t43_zfmisc_1) ).
fof(2,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/tmp/tmpdblVMp/sel_SET902+1.p_1',idempotence_k2_xboole_0) ).
fof(5,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpdblVMp/sel_SET902+1.p_1',commutativity_k2_xboole_0) ).
fof(7,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/tmp/tmpdblVMp/sel_SET902+1.p_1',l4_zfmisc_1) ).
fof(8,axiom,
! [X1] : singleton(X1) != empty_set,
file('/tmp/tmpdblVMp/sel_SET902+1.p_1',l1_zfmisc_1) ).
fof(10,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmpdblVMp/sel_SET902+1.p_1',t7_xboole_1) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(17,negated_conjecture,
? [X1,X2,X3] :
( singleton(X1) = set_union2(X2,X3)
& ( X2 != singleton(X1)
| X3 != singleton(X1) )
& ( X2 != empty_set
| X3 != singleton(X1) )
& ( X2 != singleton(X1)
| X3 != empty_set ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(18,negated_conjecture,
? [X4,X5,X6] :
( singleton(X4) = set_union2(X5,X6)
& ( X5 != singleton(X4)
| X6 != singleton(X4) )
& ( X5 != empty_set
| X6 != singleton(X4) )
& ( X5 != singleton(X4)
| X6 != empty_set ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,negated_conjecture,
( singleton(esk1_0) = set_union2(esk2_0,esk3_0)
& ( esk2_0 != singleton(esk1_0)
| esk3_0 != singleton(esk1_0) )
& ( esk2_0 != empty_set
| esk3_0 != singleton(esk1_0) )
& ( esk2_0 != singleton(esk1_0)
| esk3_0 != empty_set ) ),
inference(skolemize,[status(esa)],[18]) ).
cnf(20,negated_conjecture,
( esk3_0 != empty_set
| esk2_0 != singleton(esk1_0) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,negated_conjecture,
( esk3_0 != singleton(esk1_0)
| esk2_0 != empty_set ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(22,negated_conjecture,
( esk3_0 != singleton(esk1_0)
| esk2_0 != singleton(esk1_0) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(23,negated_conjecture,
singleton(esk1_0) = set_union2(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[19]) ).
fof(24,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[2]) ).
cnf(25,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[24]) ).
fof(32,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(33,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[32]) ).
fof(37,plain,
! [X1,X2] :
( ( ~ subset(X1,singleton(X2))
| X1 = empty_set
| X1 = singleton(X2) )
& ( ( X1 != empty_set
& X1 != singleton(X2) )
| subset(X1,singleton(X2)) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(38,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( ( X3 != empty_set
& X3 != singleton(X4) )
| subset(X3,singleton(X4)) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X3 != empty_set
| subset(X3,singleton(X4)) )
& ( X3 != singleton(X4)
| subset(X3,singleton(X4)) ) ),
inference(distribute,[status(thm)],[38]) ).
cnf(42,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(43,plain,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[8]) ).
cnf(44,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[43]) ).
fof(48,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(49,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(58,negated_conjecture,
subset(esk2_0,singleton(esk1_0)),
inference(spm,[status(thm)],[49,23,theory(equality)]) ).
cnf(59,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[49,33,theory(equality)]) ).
cnf(72,negated_conjecture,
( singleton(esk1_0) = esk2_0
| empty_set = esk2_0 ),
inference(spm,[status(thm)],[42,58,theory(equality)]) ).
cnf(76,negated_conjecture,
( esk2_0 = empty_set
| esk3_0 != empty_set ),
inference(spm,[status(thm)],[20,72,theory(equality)]) ).
cnf(77,negated_conjecture,
( esk2_0 = empty_set
| esk2_0 != esk3_0 ),
inference(spm,[status(thm)],[22,72,theory(equality)]) ).
cnf(83,negated_conjecture,
subset(esk3_0,singleton(esk1_0)),
inference(spm,[status(thm)],[59,23,theory(equality)]) ).
cnf(89,negated_conjecture,
( singleton(esk1_0) = esk3_0
| empty_set = esk3_0 ),
inference(spm,[status(thm)],[42,83,theory(equality)]) ).
cnf(94,negated_conjecture,
( esk3_0 = empty_set
| esk2_0 != empty_set ),
inference(spm,[status(thm)],[21,89,theory(equality)]) ).
cnf(100,negated_conjecture,
( esk3_0 = esk2_0
| esk2_0 = empty_set
| esk3_0 = empty_set ),
inference(spm,[status(thm)],[72,89,theory(equality)]) ).
cnf(102,negated_conjecture,
( set_union2(esk2_0,empty_set) = singleton(esk1_0)
| esk2_0 != empty_set ),
inference(spm,[status(thm)],[23,94,theory(equality)]) ).
cnf(106,negated_conjecture,
( set_union2(empty_set,esk2_0) = singleton(esk1_0)
| esk2_0 != empty_set ),
inference(rw,[status(thm)],[102,33,theory(equality)]) ).
cnf(118,negated_conjecture,
( esk3_0 = esk2_0
| esk2_0 = empty_set ),
inference(csr,[status(thm)],[100,76]) ).
cnf(119,negated_conjecture,
esk2_0 = empty_set,
inference(csr,[status(thm)],[118,77]) ).
cnf(124,negated_conjecture,
( empty_set = singleton(esk1_0)
| esk2_0 != empty_set ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[106,119,theory(equality)]),25,theory(equality)]) ).
cnf(125,negated_conjecture,
( empty_set = singleton(esk1_0)
| $false ),
inference(rw,[status(thm)],[124,119,theory(equality)]) ).
cnf(126,negated_conjecture,
empty_set = singleton(esk1_0),
inference(cn,[status(thm)],[125,theory(equality)]) ).
cnf(127,negated_conjecture,
$false,
inference(sr,[status(thm)],[126,44,theory(equality)]) ).
cnf(128,negated_conjecture,
$false,
127,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET902+1.p
% --creating new selector for []
% -running prover on /tmp/tmpdblVMp/sel_SET902+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET902+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET902+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET902+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------